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Hi,
I have a three port balun. Let's call port1 as input, port2 as output+ and port3 as output-. I can get the 3X3 s-parameter from measurement. For example, let's say for an ideal 1:1 balun here is what I get: [S11 S12 S13; S21 S22 S23; S31 S32 S33] = [1/3 -2/3 2/3; -2/3 1/3, 2/3; 2/3 2/3 1/3]. Each port is 50 Ohm in this measurement. Now I want to convert this three port s-parameter to a two port s-parameter network where port2 (output+) and port3 (output-) are considered as one port (let's call it port2'). What is the new 2X2 s-parameter for this port1 and port2'?
For my ideal balun example, in simulation, if I connect a differential 100 Ohm port between port2 and port3, I get: [S11' S12'; S21' S22'] = [1/3 sqrt(8/9); sqrt(8/9) -1/3]. If I connect a differential 50 Ohm port between port2 and port3, I get: [S11' S12'; S21' S22'] = [0 1; 1 0]. NowI want to get a mathematical expression which shows the relationship between the two cases. It doesn't matter if you assume a 50 Ohm or 100 Ohm differential. I want to use the expression in real life measurement where the balun is not ideal and symmetry might not be there. I understand there need to be some assumptions, but if you are familiar with this, I appreciate your help. Thank you.
I have a three port balun. Let's call port1 as input, port2 as output+ and port3 as output-. I can get the 3X3 s-parameter from measurement. For example, let's say for an ideal 1:1 balun here is what I get: [S11 S12 S13; S21 S22 S23; S31 S32 S33] = [1/3 -2/3 2/3; -2/3 1/3, 2/3; 2/3 2/3 1/3]. Each port is 50 Ohm in this measurement. Now I want to convert this three port s-parameter to a two port s-parameter network where port2 (output+) and port3 (output-) are considered as one port (let's call it port2'). What is the new 2X2 s-parameter for this port1 and port2'?
For my ideal balun example, in simulation, if I connect a differential 100 Ohm port between port2 and port3, I get: [S11' S12'; S21' S22'] = [1/3 sqrt(8/9); sqrt(8/9) -1/3]. If I connect a differential 50 Ohm port between port2 and port3, I get: [S11' S12'; S21' S22'] = [0 1; 1 0]. NowI want to get a mathematical expression which shows the relationship between the two cases. It doesn't matter if you assume a 50 Ohm or 100 Ohm differential. I want to use the expression in real life measurement where the balun is not ideal and symmetry might not be there. I understand there need to be some assumptions, but if you are familiar with this, I appreciate your help. Thank you.
